This email consists of some notes on the above topics.
I use an extended n-tuple notation where n is 3 or 4, 6 or 7.
My extensions are: each element of the tuple can be a list;
names do not have to be absolute URIs.
Contents:
1. View and EPS LATTICE
2. Context and ECP LATTICE
3. GenusDifferentia Definitions
4. Nothing
5. Space Time
6. Implications for OWL
7. Examples
1. View and EPS LATTICE
A View is a set of propositions. A View can be constructed
for any Ontology. It is useful to display a View as an
Entity-Property-Statement LATTICE. An EPS LATTICE can be
simplified by using subClassOf and subPropertyOf inferences and
Definitions. Statements are represented by 3-tuples.
<subject> <predicate> <object> ;
2. Context and ECP LATTICE
To combine two or more views, we need a Context mechanism to
distinguish the Views. We do this by extending the Statement
concept to a Proposition. Propositions are represented by
6-tuples
<space> <time> <view> <subject> <predicate> <object> ;
3. GenusDifferentia Definition
A GenusDifferentia Definition is a Statement which identifies
the nature of the Individuals (units) which are subsumed by
a Class (concept). Although a Definition can be composed
from 3-tuples, it is advantageous to use 4-tuples
<subject> <predicate> <object> <modifier>
The subject is the Individual or Class or Property being defined.
The predicate is individualOf or properSubClassOf or properSubPropertyOf.
The object is the genus Class of the subject.
The modifier is the differentia -- the Property restrictions which
are the essential characteristics of the subject.
The subject and object are adjacent elements in the View LATTICE.
The 4-tuple is also an excellent representation for action predicates.
In this case, modifier is a list of "adverb phrases".
4. Nothing
Since Nothing has no extension, it is not part of the View LATTICE.
5. Space Time
The View LATTICE is, in general, space-time dependent. The space,
time attributes measure changes, i.e., action predicates.
6. Implications for OWL
To represent the concepts described in these notes, OWL needs these
additional Properties.
space
time
view
instanceOf
properSubClassOf
properSubPropertyOf
isDefinedAs
7. Examples
GenusDifferentia Definitions.
<man> <isDefinedAs> <animal> <rational> ;
<woman> <isDefinedAs> <person> <sex = female> ;
<lattice> <isDefinedAs> <LATTICE> <ambiguous genus> ;
<hierarchy> <isDefinedAs> <LATTICE> <unique genus> ;
An EPS LATTICE
Thing
Entity
Person
John Doe
Mary Doe
Property
sex
male
female
Statement
<John Doe> <sex> <male> ;
<Mary Doe> <sex> <female> ;
An ECP LATTICE
Thing
Entity
Person
John Doe
Mary Doe
Dick McCullough
Characteristic
action
work
work_001
make
make_002
write
write_003
attribute
space
London
London home
Pioneer home
time
week day
6 pm
2003-05-06 5:00 pm
view
week day routine
every day routine
Semantic Web activity
sex
male
female
Proposition
<London> <week day> <week day routine>
<John Doe> <work> <work_001> <from 9 am to 5 pm> ;
<London home> <6 pm> <every day routine>
<Mary Doe> <make> <make_002> <dinner> ;
<Pioneer home> <2003-05-06 5:00 pm> <Semantic Web activity>
<Dick McCullough> <write> <write_003> <this email> ;
============
Dick McCullough
knowledge := man do identify od existent done;
knowledge haspart proposition list;